Browsing by Subject "mixing"
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Item An investigation of the influence of initial conditions on Rayleigh-Taylor mixing(Texas A&M University, 2006-04-12) Mueschke, Nicholas JayExperiments and direct numerical simulations (DNS) have been performed to examine the e??ects of initial conditions on the dynamics of a Rayleigh-Taylor unsta- ble mixing layer. Experiments were performed on a water channel facility to measure the interfacial and velocity perturbations initially present at the two-fluid interface in a small Atwood number mixing layer. The experimental measurements have been parameterized for use in numerical simulations of the experiment. Two- and three- dimensional DNS of the experiment have been performed using the parameterized initial conditions. It is shown that simulations implemented with initial velocity and density perturbations, rather than density perturbations alone, are required to match experimentally-measured statistics and spectra. Data acquired from both the exper- iment and numerical simulations are used to examine the role of initial conditions on the evolution of integral-scale, turbulence, and mixing statistics. Early-time turbu- lence and mixing statistics are shown to be strongly-dependent upon the early-time transition of the initial perturbation from a weakly-nonlinear to a strongly-nonlinear flow.Item Analysis of Topological Chaos in Ghost Rod Mixing at Finite Reynolds Numbers Using Spectral Methods(2011-02-22) Rao, Pradeep C.The effect of finite Reynolds numbers on chaotic advection is investigated for two dimensional lid-driven cavity flows that exhibit topological chaos in the creeping flow regime. The emphasis in this endeavor is to study how the inertial effects present due to small, but non-zero, Reynolds number influence the efficacy of mixing. A spectral method code based on the Fourier-Chebyshev method for two-dimensional flows is developed to solve the Navier-Stokes and species transport equations. The high sensitivity to initial conditions and the exponentional growth of errors in chaotic flows necessitate an accurate solution of the flow variables, which is provided by the exponentially convergent spectral methods. Using the spectral coefficients of the basis functions as solved through the conservation equations, exponentially accurate values of velocity everywhere in the flow domain are obtained as required for the Lagrangian particle tracking. Techniques such as Poincare maps, the stirring index based on the box counting method, and the tracking of passive scalars in the flow are used to analyze the topological chaos and quantify the mixing efficiency.Item Degree of mixing downstream of rectangular bends and design of an inlet for ambient aerosol(Texas A&M University, 2006-04-12) Seo, YoungjinTests were conducted to characterize mixing in a square and a rectangular duct with respect to suitability for single point sampling of contaminants. Several configurations, such as a straight duct with unidirectional flow at the entrance section and straight ducts preceded by mixing elements (a 90?? mitred bend, double 90?? bends in S- and U-type configurations) were tested. For a straight duct of square cross section, the COV of tracer gas concentration at 19 duct diameters downstream of the gas release location is 143% (Center release). COVs of velocity and tracer gas concentration downstream of each mixing element in square duct setups were verified throughout this study. In the case of a rectangular duct with a 3:1 (width to height) aspect ratio, COVs of velocity and tracer gas concentration only downstream of a 90?? mitred bend were verified. Tests were conducted to develop improved inlets for a Battelle bioaerosol sampling system. New inlets have been developed called the All Weather Inlets (AWI), which are designed to prevent entry of precipitation while maintaining aerosol penetration. The AWI has two inlets - one that samples at a flow rate of 780 L/min and the other one that is operated at a flow rate of 90 L/min. The initial version of the AWI-780 L/min unit featured an internal cone, which was removed because the penetration of the AWI-780 without the bottom chamber was higher than that of the Battelle inlet ?? 81% with the cone while 86% without the cone for around 9.5 ??m AD at 2 km/h. The best bug-screen configuration was verified and a cutpoint management process was performed. The inlets were tested with different wind speeds from 2 to 24 km/h to verify the wind sensitivity of those inlets.Item Effects of Single Mode Initial Conditions in Rayleigh-Taylor Turbulent Mixing(2011-02-22) Doron, YuvalThe effect of single mode initial conditions at the interface of Rayleigh-Taylor(RT) mixing are experimentally examined utilizing the low Atwood number water channel facility at Texas A&M. The water channel convects two separated stratified flows and unifies them at the end of a splitter plate. The RT instability is attained by convecting a cold stream above a warmer stream. Average density calculations are based on long time average optical measurements. The water channel was modifified with a flapper fin like device at the end of the splitter plate which was actuated by a computer controlled servo motor. Other modifications to the experiment were implemented resulting in reduced uncertainty. The experiment examined five different modes in addition to the baseline: 2 cm, 3 cm, 4 cm, 6 cm, and 8 cm wavelengths. The mixing width growth rates were shown to be dependent on initial conditions. Additionally, it appears that the growth rates commence with terminal velocity and are observed to line up with the baseline case.Item Facets for Continuous Multi-Mixing Set and Its Generalizations: Strong Cuts for Multi-Module Capacitated Lot-Sizing Problem(2014-08-20) Bansal, ManishThe research objective of this dissertation is to develop new facet-defining valid inequalities for several new multi-parameter multi-constraint mixed integer sets. These valid inequalities result in cutting planes that significantly improve the efficiency of algorithms for solving mixed integer programming (MIP) problems involving multimodule capacity constraints. These MIPs arise in many classical and modern applications ranging from production planning to cloud computing. The research in this dissertation generalizes cut-generating methods such as mixed integer rounding (MIR), mixed MIR, continuous mixing, n-step MIR, mixed n-step MIR, migling, and n-step mingling, along with various well-known families of cuts for problems such as multi-module capacitated lot-sizing (MMLS), multi-module capacitated facility location (MMFL), and multi-module capacitated network design (MMND) problems. More specifically, in the first step, we introduce a new generalization of the continuous mixing set, referred to as the continuous multi-mixing set, where the coefficients satisfy certain conditions. For each n? ? {1; : : : ; n}, we develop a class of valid inequalities for this set, referred to as the n0-step cycle inequalities, and present their facet-defining properties. We also present a compact extended formulation for this set and an exact separation algorithm to separate over the set of all n?-step cycle inequalities for a given n? ? {1; : : : ; n}. In the next step, we extend the results of the first step to the case where conditions on the coefficients of the continuous multi-mixing set are relaxed. This leads to an extended formulation and a generalization of the n-step cycle inequalities, n ? N, for the continuous multi-mixing set with general coefficients. We also show that these inequalities are facet-defining in many cases. In the third step, we further generalize the continuous multi-mixing set (where no conditions are imposed on the coefficients) by incorporating upper bounds on the integer variables. We introduce a compact extended formulation and new families of multi-row cuts for this set, referred to as the mingled n-step cycle inequalities (n ? N), through a generalization of the n-step mingling. We also provide an exact separation algorithm to separate over a set of all these inequalities. Furthermore, we present the conditions under which a subset of the mingled n-step cycle inequalities are facet-defining for this set. Finally, in the fourth step, we utilize the results of first step to introduce new families of valid inequalities for MMLS, MMFL, and MMND problems. Our computational results show that the developed cuts are very effective in solving the MMLS instances with two capacity modules, resulting in considerable reduction in the integrality gap, the number of nodes, and total solution time.Item Mixed n-Step MIR Inequalities, n-Step Conic MIR Inequalities and a Polyhedral Study of Single Row Facility Layout Problem(2012-10-19) Sanjeevi, SujeevrajaIn this dissertation, we introduce new families of valid inequalities for general linear mixed integer programs (MIPs) and second-order conic MIPs (SOCMIPs) and establish several theoretical properties and computational effectiveness of these inequalities. First we introduce the mixed n-step mixed integer rounding (MIR) inequalities for a generalization of the mixing set which we refer to as the n-mixing set. The n-mixing set is a multi-constraint mixed integer set in which each constraint has n integer variables and a single continuous variable. We then show that mixed n-step MIR can generate multi-row valid inequalities for general MIPs and special structure MIPs, namely, multi- module capacitated lot-sizing and facility location problems. We also present the results of our computational experiments with the mixed n-step MIR inequalities on small MIPLIB instances and randomly generated multi-module lot-sizing instances which show that these inequalities are quite effective. Next, we introduce the n-step conic MIR inequalities for the so-called polyhedral second-order conic (PSOC) mixed integer sets. PSOC sets arise in the polyhedral reformulation of SOCMIPs. We first introduce the n-step conic MIR inequality for a PSOC set with n integer variables and prove that all the 1-step to n-step conic MIR inequalities are facet-defining for the convex hull of this set. We also provide necessary and sufficient conditions for the PSOC form of this inequality to be valid. Then, we use the aforementioned n-step conic MIR facet to derive the n-step conic MIR inequality for a general PSOC set and provide conditions for it to be facet-defining. We further show that the n-step conic MIR inequality for a general PSOC set strictly dominates the n-step MIR inequalities written for the two linear constraints that define the PSOC set. We also prove that the n-step MIR inequality for a linear mixed integer constraint is a special case of the n-step conic MIR inequality. Finally, we conduct a polyhedral study of the triplet formulation for the single row facility layout problem (SRFLP). For any number of departments n, we prove that the dimension of the triplet polytope (convex hull of solutions to the triplet formulation) is n(n - 1)(n - 2)/3. We then prove that several valid inequalities presented in Amaral (2009) for this polytope are facet-defining. These results provide theoretical support for the fact that the linear program solved over these valid inequalities gives the optimal solution for all instances studied by Amaral (2009).Item Numerical modeling of species transport in turbulent flow and experimental study on aerosol sampling(Texas A&M University, 2007-04-25) Vijayaraghavan, Vishnu KarthikNumerical simulations were performed to study the turbulent mixing of a scalar species in straight tube, single and double elbow flow configurations. Different Reynolds Averaged Navier Stokes (RANS) and Large Eddy Simulation (LES) models were used to model the turbulence in the flow. Conventional and dynamic Smagorinsky sub-grid scale models were used for the LES simulations. Wall functions were used to resolve the near wall boundary layer. These simulations were run with both two-dimensional and three-dimensional geometries. The velocity and tracer gas concentration Coefficient of Variations were compared with experimental results. The results from the LES simulations compared better with experimental results than the results from the RANS simulations. The level of mixing downstream of a S-shaped double elbow was higher than either the single elbow or the U-shaped double elbow due to the presence of counter rotating vortices. Penetration of neutralized and non-neutralized aerosol particles through three different types of tubing was studied. The tubing used included standard PVC pipes, aluminum conduit and flexible vacuum hose. Penetration through the aluminum conduit was unaffected by the presence or absence of charge neutralization, whereas particle penetrations through the PVC pipe and the flexible hosing were affected by the amount of particle charge. The electric field in a space enclosed by a solid conductor is zero. Therefore charged particles within the conducting aluminum conduit do not experience any force due to ambient electric fields, whereas the charged particles within the non-conducting PVC pipe and flexible hose experience forces due to the ambient electric fields. This increases the deposition of charged particles compared to neutralized particles within the 1.5?????? PVC tube and 1.5?????? flexible hose. Deposition 2001a (McFarland et al. 2001) software was used to predict the penetration through transport lines. The prediction from the software compared well with experiments for all cases except when charged particles were transported through non-conducting materials. A Stairmand cyclone was designed for filtering out large particles at the entrance of the transport section.Item Observations and modeling of mixing processes in a fresh water reservoir - Valle de Bravo (Mexico)(Texas A&M University, 2007-04-25) Singhal, GauravCurrent understanding of small-scale physical processes, such as mixing, in tropical water bodies is lacking and observations are scarce at best. This study sheds more light on these processes through a combined observational-modeling approach. For this purpose, observations were made in Valle de Bravo's freshwater reservoir, about 100 km west of Mexico City and at an elevation of 1830 m above sea surface. Turbulence kinetic energy dissipation (TKED) rates were estimated by fitting a theoretical Batchelor spectrum to the temperature gradient spectrum. From similarity scaling of dissipation rates, it was found that in the surface layer, winds were the main driving force in generating turbulence during the day, while convective forces were responsible during the night. Bottom boundary layer (BBL) mixing was mainly driven by internal wave (first vertical and first horizontal mode) breaking at the bottom. Lognormality of turbulence dissipation rates is also discussed for surface, intermediate and bottom boundary layers. For our modeling efforts, a state-of-the-art one-dimensional turbulence model was used and forced with the observed surface meteorology to obtain simulated temperature and dissipation rate profiles. The model results were found to be in good agreement with the observations, though minor differences in dissipation rates were found in the vicinity of the thermocline and the BBL.Item Quantification of chaotic mixing in microfluidic systems(Texas A&M University, 2004-11-15) Kim, Ho JunPeriodic and chaotic dynamical systems follow deterministic equations such as Newton's laws of motion. To distinguish the difference between two systems, the initial conditions have an important role. Chaotic behaviors or dynamics are characterized by sensitivity to initial conditions. Mathematically, a chaotic system is defined as a system very sensitive to initial conditions. A small difference in initial conditions causes unpredictability in the final outcome. If error is measured from the initial state, the relative error grows exponentially. Prediction becomes impossible and finally, chaotic systems can come to become stochastic system. To make chaotic motion, the number of variables in the system should be above three and there should be non-linear terms coupling several of the variables in the equation of motion. Phase space is defined as the space spanned by the coordinate and velocity vectors. In our case, mixing zone is phase space. With the above characteristics - the initial condition sensitivity of a chaotic system, our plan is to find most efficient chaotic stirrer. In this thesis, we present four methods to measure mixing state based on the chaotic dynamics theory. The Lyapunov exponent is a measure of the sensitivity to initial conditions and can be used to calculate chaotic strength. We can decide the chaotic state with one real number and measure efficiency of the chaotic mixer and find the optimum frequency. The Poincare section method provides a means for viewing the phase space diagram so that the motion is observed periodically. To do this, the trajectory is sectioned at regular intervals. With the Poincare section method, we can find 'islands' considered as bad mixed zones so that the mixing state can be measured qualitatively. With the chaotic dynamics theory, the initial length of the interface can grow exponentially in a chaotic system. We will show the above characteristics of the chaotic system to prove as fact that our model is an efficient chaotic mixer. The final goal for making chaotic stirrer is how to implement efficient dispersed particles. The box counting method is focused on measurement of the particles dispersing state. We use snap shots of the mixing process and with these snap shots, we devise a plan to measure particles' dispersing rate using the box-counting method.Item WIND-DRIVEN NEAR INERTIAL OCEAN RESPONSE AND MIXING AT THE CRITICAL LATITUDE(2010-07-14) Zhang, XiaoqianThe spatial structure and temporal evolution of sea breeze and the latitudinal distribution of propagation and mixing of sea breeze driven near-inertial ocean response in the Gulf of Mexico are investigated using comprehensive data sets and a non-linear numerical model. Near 30?N, inertial oceanic response is significantly enhanced by a near-resonant condition between inertial and diurnal forcing frequencies. Observational results indicate that sea breeze variability peaks in summer and extends at least 300 km offshore with continuous seaward phase propagation. The maximum near-inertial oceanic response occurs in June when there is a shallow mixed layer, strong stratification, and an approximately 10-day period of continuous sea breeze forcing. Near-inertial current variance decreases in July and August due to the deepening of the mixed layer and a more variable phase relationship between the wind and current. River discharge varies interannually and can significantly alter the oceanic response during summer. During 1993, the ?great flood? of the Mississippi River deepens the summer mixed layer and reduces the sea breeze response. The near-inertial currents can provide considerable vertical mixing on the shelf in summer, as seen by the suppression of bulk Richardson number during strong near-inertial events. Three-dimensional idealized simulations show that the coastal oceanic response to sea breeze is trapped poleward of 30? latitude, however, it can propagate offshore as Poincare waves equatorward of 30? latitude. Near 30? latitude, the maximum oceanic response to sea breeze moves offshore slowly because of the near-zero group speed of Poincare waves at this latitude. The lateral energy flux convergence plus the energy input from the wind is maximum near the critical latitude, leading to increased vertical mixing. This local dissipation is greatly reduced at other latitudes. Simulations with realistic bathymetry of the Gulf of Mexico confirm that a basin-wide ocean response to coastal sea breeze forcing is established in the form of Poincare waves. This enhanced vertical mixing is consistent with observations on the Texas-Louisiana Shelf. Comparison of the three-dimensional and one-dimensional models shows some significant limitations of one-dimensional simplified models for sea breeze simulations near the critical latitude.